WS10 berekening 7 TVD

*The author of this computation has been verified*

R Software Module: /rwasp_arimaforecasting.wasp (opens new window with default values)

Title produced by software: ARIMA Forecasting

Date of computation: Wed, 09 Dec 2009 10:42:31 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/09/t1260380605vd73xophde2v8lw.htm/, Retrieved Wed, 09 Dec 2009 18:43:27 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/09/t1260380605vd73xophde2v8lw.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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101.3 106.3 94 102.8 102 105.1 92.4 81.4 105.8 120.3 100.7 88.8 94.3 99.9 103.4 103.3 98.8 104.2 91.2 74.7 108.5 114.5 96.9 89.6 97.1 100.3 122.6 115.4 109 129.1 102.8 96.2 127.7 128.9 126.5 119.8 113.2 114.1 134.1 130 121.8 132.1 105.3 103 117.1 126.3 138.1 119.5 138 135.5 178.6 162.2 176.9 204.9 132.2 142.5 164.3 174.9 175.4 143

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Univariate ARIMA Extrapolation Forecast time Y[t] F[t] 95% LB 95% UB p-value (H0: Y[t] = F[t]) P(F[t]>Y[t-1]) P(F[t]>Y[t-s]) P(F[t]>Y[32]) 20 74.7 - - - - - - - 21 108.5 - - - - - - - 22 114.5 - - - - - - - 23 96.9 - - - - - - - 24 89.6 - - - - - - - 25 97.1 - - - - - - - 26 100.3 - - - - - - - 27 122.6 - - - - - - - 28 115.4 - - - - - - - 29 109 - - - - - - - 30 129.1 - - - - - - - 31 102.8 - - - - - - - 32 96.2 - - - - - - - 33 127.7 122.5071 100.67 153.0465 0.3695 0.9543 0.8157 0.9543 34 128.9 129.5576 104.3393 166.1645 0.486 0.5396 0.7899 0.963 35 126.5 111.4923 91.1338 140.2429 0.1531 0.1177 0.8401 0.8514 36 119.8 99.2789 81.7185 123.7624 0.0502 0.0147 0.7808 0.5973 37 113.2 99.908 79.409 130.4073 0.1965 0.1006 0.5716 0.5942 38 114.1 108.4604 81.8573 152.1938 0.4002 0.4159 0.6427 0.7087 39 134.1 114.1972 84.0485 166.3071 0.227 0.5015 0.376 0.7508 40 130 111.9233 82.1655 163.6228 0.2466 0.2002 0.4476 0.7244 41 121.8 106.7994 78.57 155.6342 0.2736 0.1759 0.4648 0.6647 42 132.1 104.8799 76.5008 154.8328 0.1428 0.2534 0.171 0.6333 43 105.3 106.7303 76.3983 162.2269 0.4799 0.1851 0.5552 0.645 44 103 109.3139 76.8615 170.953 0.4204 0.5508 0.6617 0.6617 45 117.1 109.8184 76.4363 174.6047 0.4128 0.5817 0.2943 0.6598 46 126.3 108.453 75.0955 173.914 0.2965 0.3979 0.2702 0.6431 47 138.1 107.2304 73.7891 173.7396 0.1815 0.2871 0.2851 0.6274 48 119.5 107.2773 73.0938 176.7411 0.3651 0.1922 0.3619 0.6227 49 138 108.1008 72.8158 181.6309 0.2127 0.3806 0.4459 0.6245 50 135.5 108.63 72.4573 185.6738 0.2471 0.2275 0.4447 0.6241 51 178.6 108.4457 71.7971 187.8203 0.0416 0.252 0.2632 0.6188 52 162.2 107.9794 71.0134 189.2587 0.0955 0.0443 0.2977 0.6118 53 176.9 107.7855 70.3595 191.4874 0.0528 0.1013 0.3714 0.6069 54 204.9 107.9562 69.8878 194.7397 0.0143 0.0597 0.2928 0.6047 55 132.2 108.1978 69.4728 198.1754 0.3005 0.0176 0.5252 0.6031 56 142.5 108.2493 68.9954 201.0486 0.2347 0.3065 0.5441 0.6004 57 164.3 108.1269 68.4552 203.4197 0.124 0.2398 0.4268 0.5969 58 174.9 108.0112 67.9278 205.8374 0.0901 0.1297 0.357 0.5935 59 175.4 108.0127 67.4619 208.6362 0.0947 0.0963 0.2789 0.591 60 143 108.0888 67.0417 211.6788 0.2545 0.1014 0.4145 0.589 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.1272 0.0424 0 26.9665 0 0 34 0.1442 -0.0051 0.0237 0.4325 13.6995 3.7013 35 0.1316 0.1346 0.0607 225.23 84.2097 9.1766 36 0.1258 0.2067 0.0972 421.1153 168.4361 12.9783 37 0.1558 0.133 0.1044 176.6772 170.0843 13.0416 38 0.2057 0.052 0.0956 31.8054 147.0378 12.1259 39 0.2328 0.1743 0.1069 396.1197 182.6209 13.5137 40 0.2357 0.1615 0.1137 326.7675 200.6393 14.1647 41 0.2333 0.1405 0.1167 225.0183 203.348 14.26 42 0.243 0.2595 0.131 740.9319 257.1064 16.0345 43 0.2653 -0.0134 0.1203 2.0458 233.9191 15.2944 44 0.2877 -0.0578 0.1151 39.8651 217.7479 14.7563 45 0.301 0.0663 0.1113 53.0219 205.0767 14.3205 46 0.308 0.1646 0.1151 318.5169 213.1796 14.6007 47 0.3165 0.2879 0.1266 952.9352 262.4966 16.2017 48 0.3304 0.1139 0.1258 149.3943 255.4277 15.9821 49 0.347 0.2766 0.1347 893.9623 292.9886 17.1169 50 0.3619 0.2474 0.141 721.9946 316.8222 17.7995 51 0.3734 0.6469 0.1676 4921.6247 559.1803 23.647 52 0.384 0.5021 0.1843 2939.8746 678.215 26.0426 53 0.3962 0.6412 0.2061 4776.82 873.3866 29.5531 54 0.4101 0.898 0.2375 9398.1042 1260.8738 35.5088 55 0.4243 0.2218 0.2368 576.1079 1231.1014 35.0871 56 0.4374 0.3164 0.2402 1173.1088 1228.685 35.0526 57 0.4496 0.5195 0.2513 3155.4154 1305.7542 36.1352 58 0.4621 0.6193 0.2655 4474.1068 1427.614 37.7838 59 0.4753 0.6239 0.2788 4541.0496 1542.9264 39.2801 60 0.489 0.323 0.2803 1218.7947 1531.3503 39.1325

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260380605vd73xophde2v8lw/1n3rv1260380549.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260380605vd73xophde2v8lw/1n3rv1260380549.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260380605vd73xophde2v8lw/25adz1260380549.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260380605vd73xophde2v8lw/25adz1260380549.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ; par5 = 1 ; par6 = 1 ; par7 = 0 ; par8 = 11 ;

Parameters (R input):

par1 = 12 ; par2 = -0.6 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) #cut off periods par1 <- 28 par2 <- as.numeric(par2) #lambda par3 <- as.numeric(par3) #degree of non-seasonal differencing par4 <- as.numeric(par4) #degree of seasonal differencing par5 <- as.numeric(par5) #seasonal period par6 <- as.numeric(par6) #p par6 <- 3 par7 <- as.numeric(par7) #q par7 <- 3 par8 <- as.numeric(par8) #P par9 <- as.numeric(par9) #Q if (par10 == 'TRUE') par10 <- TRUE if (par10 == 'FALSE') par10 <- FALSE if (par2 == 0) x <- log(x) if (par2 != 0) x <- x^par2 lx <- length(x) first <- lx - 2*par1 nx <- lx - par1 nx1 <- nx + 1 fx <- lx - nx if (fx < 1) { fx <- par5 nx1 <- lx + fx - 1 first <- lx - 2*fx } first <- 1 if (fx < 3) fx <- round(lx/10,0) (arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML')) (forecast <- predict(arima.out,par1)) (lb <- forecast$pred - 1.96 * forecast$se) (ub <- forecast$pred + 1.96 * forecast$se) if (par2 == 0) { x <- exp(x) forecast$pred <- exp(forecast$pred) lb <- exp(lb) ub <- exp(ub) } if (par2 != 0) { x <- x^(1/par2) forecast$pred <- forecast$pred^(1/par2) lb <- lb^(1/par2) ub <- ub^(1/par2) } if (par2 < 0) { olb <- lb lb <- ub ub <- olb } (actandfor <- c(x[1:nx], forecast$pred)) (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) bitmap(file='test1.png') opar <- par(mar=c(4,4,2,2),las=1) ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub)) plot(x,ylim=ylim,type='n',xlim=c(first,lx)) usr <- par('usr') rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon') rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender') abline(h= (-3:3)*2 , col ='gray', lty =3) polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA) lines(nx1:lx, lb , lty=2) lines(nx1:lx, ub , lty=2) lines(x, lwd=2) lines(nx1:lx, forecast$pred , lwd=2 , col ='white') box() par(opar) dev.off() prob.dec <- array(NA, dim=fx) prob.sdec <- array(NA, dim=fx) prob.ldec <- array(NA, dim=fx) prob.pval <- array(NA, dim=fx) perf.pe <- array(0, dim=fx) perf.mape <- array(0, dim=fx) perf.mape1 <- array(0, dim=fx) perf.se <- array(0, dim=fx) perf.mse <- array(0, dim=fx) perf.mse1 <- array(0, dim=fx) perf.rmse <- array(0, dim=fx) for (i in 1:fx) { locSD <- (ub[i] - forecast$pred[i]) / 1.96 perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i] perf.se[i] = (x[nx+i] - forecast$pred[i])^2 prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD) prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD) prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD) prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD) } perf.mape[1] = abs(perf.pe[1]) perf.mse[1] = abs(perf.se[1]) for (i in 2:fx) { perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i]) perf.mape1[i] = perf.mape[i] / i perf.mse[i] = perf.mse[i-1] + perf.se[i] perf.mse1[i] = perf.mse[i] / i } perf.rmse = sqrt(perf.mse1) bitmap(file='test2.png') plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub))) dum <- forecast$pred dum[1:par1] <- x[(nx+1):lx] lines(dum, lty=1) lines(ub,lty=3) lines(lb,lty=3) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'time',1,header=TRUE) a<-table.element(a,'Y[t]',1,header=TRUE) a<-table.element(a,'F[t]',1,header=TRUE) a<-table.element(a,'95% LB',1,header=TRUE) a<-table.element(a,'95% UB',1,header=TRUE) a<-table.element(a,'p-value<br />(H0: Y[t] = F[t])',1,header=TRUE) a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE) a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE) mylab <- paste('P(F[t]>Y[',nx,sep='') mylab <- paste(mylab,'])',sep='') a<-table.element(a,mylab,1,header=TRUE) a<-table.row.end(a) for (i in (nx-par5):nx) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,x[i]) a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.row.end(a) } for (i in 1:fx) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,round(x[nx+i],4)) a<-table.element(a,round(forecast$pred[i],4)) a<-table.element(a,round(lb[i],4)) a<-table.element(a,round(ub[i],4)) a<-table.element(a,round((1-prob.pval[i]),4)) a<-table.element(a,round((1-prob.dec[i]),4)) a<-table.element(a,round((1-prob.sdec[i]),4)) a<-table.element(a,round((1-prob.ldec[i]),4)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'time',1,header=TRUE) a<-table.element(a,'% S.E.',1,header=TRUE) a<-table.element(a,'PE',1,header=TRUE) a<-table.element(a,'MAPE',1,header=TRUE) a<-table.element(a,'Sq.E',1,header=TRUE) a<-table.element(a,'MSE',1,header=TRUE) a<-table.element(a,'RMSE',1,header=TRUE) a<-table.row.end(a) for (i in 1:fx) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,round(perc.se[i],4)) a<-table.element(a,round(perf.pe[i],4)) a<-table.element(a,round(perf.mape1[i],4)) a<-table.element(a,round(perf.se[i],4)) a<-table.element(a,round(perf.mse1[i],4)) a<-table.element(a,round(perf.rmse[i],4)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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